Multi-perspective modelling of complex phenomena

This conceptual paper discusses the limitations of a single-perspective hierarchical approach to modelling and proposes multi-perspective modelling as a way to overcome them. As it turns out, multi-perspective modelling is primarily a new methodology, using existing modelling techniques but extending the modelling hierarchy with a new epistemological level which integrates the different perspectives. The methodology will be presented in some detail, and its use will be demonstrated by analyzing an example taken from a socio-political context.     

GMDH algorithms for complex systems modelling

At present, GMDH algorithms give us a way to identify and forecast economic processes in the case of noised and short input sampling. In contrast to neural networks, the results are explicit mathematical models, obtained in a relatively short time. For ill-defined objects with very big noises, better results are obtained by analog complexing methods. Nets with active neurons should be applied to increase accuracy. Active neurons are able, during the self-organizing process, to estimate which inputs are necessary to minimize the given objective function of the neuron. In the neuronet with such neurons, we have a twofold multilayered structure: neurons themselves are multilayered, and they will be united into a multilayered network.

SelfOrganize! is an easy-to-use modelling tool which realizes twice-multilayered neu-ronets and enables the creation of time series, single input/single output, multi-input/single output and multi-input/multi-output systems (system of equations). Successful applications are shown in the field of analysis and prediction of characteristics of stock markets in financial risk control modelling.     

Mathematical modelling of hydraulic transients in complex systems

It is a very well-known fact that calculations necessary to analyze transient conditions in hydraulic systems are very time-consuming and difficult to organize, especially in complex systems. Nevertheless, such calculations are necessary to achieve efficiency and economy in the design and operation, as well as safety in these systems, since those objectives need precise calculations of pressures and flowrates. Suitable mathematical modeling of the different elements in a hydraulic system is necessary to get useful results, which help fulfill those objectives. In this paper, the mathematical model described in [1] is generalized to complex pressurized hydraulic systems. To model the behavior of the fluid within the ducts, use is made of the so-called elastic model, which is numerically solved by the methods of characteristics. Nevertheless, the main objective of this paper hinges on the treatment of the boundary conditions that allow developing a general model virtually representing every combination of elements at a given location of the system. The final objective is to provide the users with a powerful tool to devise the potential risks to which an installation may be exposed and to develop suitable protection strategies.     

Scaffolding and metacognition

This paper proposes an expanded conception of scaffolding with four key elements: i. scaffolding agency – expert, reciprocal, and self-scaffolding;

ii. scaffolding domain – conceptual and heuristic scaffolding;

iii. the identification of self-scaffolding with metacognition; and

iv. the identification of six zones of scaffolding activity; each zone distinguished by the matter under construction and the relative positioning of the participant(s) in the act of scaffolding.

These key elements are illustrated with empirical examples drawn from a variety of research studies. Scaffolding, thus conceived, brings together several theoretical domains, and by situating metacognition within a framework derived from the social activity of scaffolding, a bridge is formed between the instructional support a teacher might provide and the learner's self-control of the learning process. With regard to instruction and the role of the teacher, it is the authors’ contention that a major object of instruction is the progressive relocation of scaffolding agency in the direction of the learner with the long-term goal of equipping the learner to take control of their own learning.     

Maintenance manpower modelling for a hospital building complex

A building maintenance manpower simulation model is developed within the case context of a specific hospital complex to investigate the potential gain to be realised using different manpower management and operational procedures. Allowance is made for daily variation in demand for maintenance, sickness and holiday patterns, and the characteristic of different trades. Numerical results are presented for the plumbing trade as a particular example of modelling output.     

The theory of self-organization and modelling complex urban systems

In this article we focus on the problem the social scientist is confronted with when trying to model the complex and dynamic world he lives and works in, and on the different scientific paradigms of the ‘hard sciences’ which are at his disposition. We further concentrate our attention on the EMUS (=Evolutionary Models of Urban Systems) models which we developed using the concepts of the theory of Self-Organization and which we believe to be capable of unravelling some of the complexity of the real world. We will not dwell on the mathematical foundations of the model, but concentrate on the philosophical basis, some practical considerations about modelling and forecasting and on results we obtained on different spatial scales and in different socio-economic contexts.     

Continuous dependence on modelling for a complex Ginzburg–Landau equation with complex coefficients

Continuous dependence on a modelling parameter is established for solutions of a problem for a complex Ginzburg–Landau equation. A homogenizing boundary condition is also used to discuss the continuous dependence results. We derive a priori estimates that indicate that solutions depend continuously on a parameter in the governing differential equation. Copyright © 2004 John Wiley & Sons, Ltd.     

Emergency and on-demand health care: modelling a large complex system

This paper describes how system dynamics was used as a central part of a whole-system review of emergency and on-demand health care in Nottingham, England. Based on interviews with 30 key individuals across health and social care, a ‘conceptual map’ of the system was developed, showing potential patient pathways through the system. This was used to construct a stock-flow model, populated with current activity data, in order to simulate patient flows and to identify system bottle-necks. Without intervention, assuming current trends continue, Nottingham hospitals are unlikely to reach elective admission targets or achieve the government target of 82% bed occupancy. Admissions from general practice had the greatest influence on occupancy rates. Preventing a small number of emergency admissions in elderly patients showed a substantial effect, reducing bed occupancy by 1% per annum over 5 years. Modelling indicated a range of undesirable outcomes associated with continued growth in demand for emergency care, but also considerable potential to intervene to alleviate these problems, in particular by increasing the care options available in the community.     

Stochastic dynamo in critical situations

Based on the functional method of consecutive approximations, we consider the problem of magnetic field excitation (stochastic dynamo) by a random velocity field with a finite temporal correlation radius. In critical situations, in the first (diffusion) approximation, the Lyapunov characteristic parameter of the magnetic field energy vanishes. This implies the absence of structure formation (clustering) in realizations of the magnetic field in that approximation. Critical situations occur in problems of magnetic field diffusion in an equilibrium thermal and random pseudoequilibrium and acoustic (in the absence of dissipation) velocity fields. The sign of the Lyapunov characteristic parameter in the second-order approximation determines the possibility of clustering of the magnetic field energy. We show that energy clustering does not occur in a thermal velocity field. In the cases of pseudoequilibrium and acoustic velocity fields, clustering occurs with probability one, i.e., in almost every realization. We evaluate the characteristic time for clustering to be established.     

Benefit sharing in holding situations

A situation is studied where one agent has available an amount of storage facility and the other agents have some goods, part of which can be stored generating benefits. The problem of sharing the benefits produced by full cooperation between agents is tackled in this paper, by introducing a related cooperative game. This game turns out to be a big boss game with interesting theoretical properties. A solution concept, relying on optimal storage plans and associated holding prices, is also introduced, and its relationship with the core of the above holding game is explored in detail. The family of monotonic decreasing bijective mappings, defined on the set of non-negative real numbers, plays an important role in our approach.     

Link formation in cooperative situations

In this paper we study the endogenous formation of cooperation structures or communication graphs between players in a superadditive TU game. For each cooperation structure that is formed, the payoffs to the players are determined by an exogenously given solution. We model the process of cooperation structure formation as a game in strategic form. It is shown that several equilibrium refinements predict the formation of the complete cooperation structure or some structure which is payoff-equivalent to the complete structure. These results are obtained for a large class of solutions for cooperative games with cooperation structures. Received September 1995/Revised version I October 1996/Revised version II April 1997/Final version September 1997     

Triangulating Smooth Submanifolds with Light Scaffolding

We propose an algorithm to sample and mesh a k-submanifold M{\mathcal{M}} of positive reach embedded in \mathbbR^d{\mathbb{R}^{d}} . The algorithm first constructs a crude sample of M{\mathcal{M}} . It then refines the sample according to a prescribed parameter e{\varepsilon} , and builds a mesh that approximates M{\mathcal{M}} . Differently from most algorithms that have been developed for meshing surfaces of \mathbbR ³{\mathbb{R} ^3} , the refinement phase does not rely on a subdivision of \mathbbR ^d{\mathbb{R} ^d} (such as a grid or a triangulation of the sample points) since the size of such scaffoldings depends exponentially on the ambient dimension d. Instead, we only compute local stars consisting of k-dimensional simplices around each sample point. By refining the sample, we can ensure that all stars become coherent leading to a k-dimensional triangulated manifold [^(M)]{\hat{\mathcal{M}}} . The algorithm uses only simple numerical operations. We show that the size of the sample is O(e^-k){O(\varepsilon ^{-k})} and that [^(M)]{\hat{\mathcal{M}}} is a good triangulation of M{\mathcal{M}} . More specifically, we show that M{\mathcal{M}} and [^(M)]{\hat{\mathcal{M}}} are isotopic, that their Hausdorff distance is O(e²){O(\varepsilon ^{2})} and that the maximum angle between their tangent bundles is O(e){O(\varepsilon )} . The asymptotic complexity of the algorithm is T(e) = O(e^-k2-k){T(\varepsilon) = O(\varepsilon ^{-k^2-k})} (for fixed M, d{\mathcal{M}, d} and k).     

Multi-issue allocation situations

This paper introduces a new class of transferable utility games, called multi-issue allocation games. These games arise from various allocation situations and are based on the concepts underlying the bankruptcy model, as introduced by O'Neill [Math. Social Sci. 2 (1982) 345]. In this model, a perfectly divisible good (estate) has to be divided amongst a given set of agents, each of whom has some claim on the estate. Contrary to the standard bankruptcy model, the current model deals with situations in which the agents' claims are multi-dimensional, where the dimensions correspond to various issues.It is shown that the class of multi-issue allocation games coincides with the class of (non-negative) exact games. The run-to-the-bank rule is introduced as a solution for multi-issue allocation situations and turns out to be Shapley value of the corresponding game. Finally, this run-to-the-bank rule is characterised by means of a consistency property in the spirit of O'Neill.     

Multi-stage sequencing situations

This paper introduces the idea of dynamics in cooperative games. The concrete case of multi-stage sequencing situations and the difficulties involved in defining stable cost savings allocations for the games arising from these situations is studied. The MEGS-rule is defined and proven to yield stable allocations. A characterization for the MEGS-rule is given.     

Numerical modelling of free-surface shallow flows over irregular topography with complex geometry

A well-balanced Godunov-type finite volume algorithm is developed for modelling free-surface shallow flows over irregular topography with complex geometry. The algorithm is based on a new formulation of the classical shallow water equations in hyperbolic conservation form. Unstructured triangular grids are used to achieve the adaptability of the grid to the geometry of the problem and to facilitate localised refinement. The numerical fluxes are calculated using HLLC approximate Riemann solver, and the MUSCL-Hancock predictor–corrector scheme is adopted to achieve the second-order accuracy both in space and in time where the solutions are continuous, and to achieve high-resolution results where the solutions are discontinuous. The novelties of the algorithm include preserving well-balanced property without any additional correction terms and the wet/dry front treatments. The good performance of the algorithm is demonstrated by comparing numerical and theoretical results of several benchmark problems, including the preservation of still water over a two-dimensional hump, the idealised dam-break flow over a frictionless flat rectangular channel, the circular dam-break, and the shock wave from oblique wall. Besides, two laboratory dam-break cases are used for model validation. Furthermore, a practical application related to dam-break flood wave propagation over highly irregular topography with complex geometry is presented. The results show that the algorithm can correctly account for free-surface shallow flows with respect to its effectiveness and robustness thus has bright application prospects.